Abstract
In this paper we discuss the semantics of adjectives from the perspective of a Modern Type Theory (MTT) with an adequate subtyping mechanism. In an MTT, common nouns (CNs) can be interpreted as types and, in particular, CNs modified by intersective and subsective adjectives can be given semantics by means of Σ-types. However, an interpretation of CNs as types would not be viable without a proper notion of subtyping which, as we explain, is given by coercive subtyping, an adequate notion of subtyping for MTTs. It is also shown that suitable uses of universes are one of the key ingredients that have made such an analysis adequate. Privative and non-committal adjectives require different treatments than the use of Σ-types. We propose to deal with privative adjectives using the disjoint union type while non-committal adjectives by making use of the type-theoretical notion of context, as used by Ranta [27] to approximate the model-theoretic notion of a possible world. Our approach to adjectives has a number of advantages over those proposed within the Montagovian setting, one of which is that the inferences related with the adjectives arise via typing and not by some kind of extra semantic meaning in the form of a meaning postulate.
This work is supported by the research grant F/07-537/AJ of the Leverhulme Trust in the U.K.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Asher, N.: Lexical Meaning in Context: a Web of Words. Cambridge University Press (2012)
Boldini, P.: Formalizing context in intuitionistic type theory. Fundamenta Informaticae 42(2), 1–23 (2000)
Chatzikyriakidis, S., Luo, Z.: An account of natural language coordination in type theory with coercive subtyping. In: Proc. of Constraint Solving and Language Processing, Orleans (2012)
Chatzikyriakidis, S., Luo, Z.: Natural Language Inference Using Coq (2013) (manuscript)
Church, A.: A formulation of the simple theory of types. J. Symbolic Logic 5(1) (1940)
Davidson, D.: Compositionality and coercion in semantics: The semantics of adjective meaning. In: Rescher, N. (ed.) The Logical Form of Action Sentences, pp. 81–95. University of Pittsburgh Press (1967)
Girard, J.Y.: Une extension de l’interpretation fonctionelle de gödel à l’analyse et son application à l’élimination des coupures dans et la thèorie des types’. In: Proc. 2nd Scandinavian Logic Symposium, North-Holland (1971)
Gupta, A.: The Logic of Common Nouns. Yale University Press (1980)
Jespersen, B., Primiero, G.: Alleged assassins: realist and constructivist semantics for modal modification. In: Bezhanishvili, G., Lbner, S., Marra, V., Richter, F. (eds.) 9th International Tbilisi Symposium on Logic, Language, and Computation (2012)
Kamp, H.: Formal semantics of natural language. In: Keenan, E. (ed.) Two Theories About Adjectives, pp. 123–155. Cambridge University Press (1975)
Larson, R.: Events and modification in nominals. In: Proceedings of Semantics and Linguistic Theory (SALT) VIII, Tokyo (1998)
Luo, Z.: Computation and Reasoning: A Type Theory for Computer Science. Oxford Univ. Press (1994)
Luo, Z.: Coercive subtyping. Journal of Logic and Computation 9(1), 105–130 (1999)
Luo, Z.: Type-theoretical semantics with coercive subtyping. Semantics and Linguistic Theory 20 (SALT20), Vancouver (2010)
Luo, Z.: Contextual analysis of word meanings in type-theoretical semantics. In: Pogodalla, S., Prost, J.-P. (eds.) LACL 2011. LNCS, vol. 6736, pp. 159–174. Springer, Heidelberg (2011)
Luo, Z.: Common nouns as types. In: Béchet, D., Dikovsky, A. (eds.) LACL 2012. LNCS, vol. 7351, pp. 173–185. Springer, Heidelberg (2012)
Luo, Z.: Formal semantics in modern type theories with coercive subtyping. Linguistics and Philosophy 35(6) (2012)
Luo, Z., Soloviev, S., Xue, T.: Coercive subtyping: theory and implementation. Information and Computation 223 (2012)
Luo, Z.: Adjectives and adverbs in type-theoretical semantics. Notes (2011)
Martin-Löf, P.: An intuitionistic theory of types: predicative part. In: Rose, H., Shepherdson, J.C. (eds.) Logic Colloquium’73 (1975)
Martin-Löf, P.: Intuitionistic Type Theory. Bibliopolis (1984)
Montague, R.: The proper treatment of quantification in ordinary English. In: Hintikka, J., Moravcsik, J., Suppes, P. (eds.) Approaches to Natural Languages (1973)
Montague, R.: Formal Philosophy. Yale University Press (1974)
Partee, B.: Compositionality and coercion in semantics: The semantics of adjective meaning. In: Bouma, G., Krämer, I., Zwarts, J. (eds.) Cognitive Foundations of Interpretation, Royal Netherlands Academy of Arts and Sciences (2007)
Partee, B.: Presuppositions and discourse: Essays offered to hans kamp. In: Bauerle, R., Reyle, U. (eds.) Privative Adjectives: Subsective Plus Coercion, pp. 123–155. Emerald Group Publishing (2010)
Ranta, A.: Constructing possible worlds. Theoria 52(1-2), 77–99 (1991)
Ranta, A.: Type-Theoretical Grammar. Oxford University Press (1994)
Sundholm, G.: Proof theory and meaning. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic III: Alternatives to Classical Logic. Reidel (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chatzikyriakidis, S., Luo, Z. (2013). Adjectives in a Modern Type-Theoretical Setting. In: Morrill, G., Nederhof, MJ. (eds) Formal Grammar. FG FG 2013 2012. Lecture Notes in Computer Science, vol 8036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39998-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-39998-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39997-8
Online ISBN: 978-3-642-39998-5
eBook Packages: Computer ScienceComputer Science (R0)